The body of the paper is organized as follows. Section  is motivated by the problem of robotic following of planar curves
and offers a number of technical and relevant to the issue facts about their kinematics.
Section  addresses kinematics of isosurfaces and is inspired by the problem
of their sweeping coverage in the case of a time-varying environmental field in 3D.
Section REF  presents a technical fact that extends Theorem 4.1 in Chapter III [1]} on ODE with discontinuous right-hand sides.
